You can do it manually.
If you put ammo for the sniper in a backpack, drop it on the ground and give him the order to pick it up (select the sniper with "F#", press "6", chose "Take Backpack" in the list).
The second way to do it, is to put the ammo manually in a vehicle and tell the sniper rearm at that specific vehicle (select the sniper with "F#", press "6", chose "Rearm at *vehicle*).

That procedure can be used to rearm any unit, with any ammo. The only thing you need to unlock is the Amour, which should be the first thing to unlock anyway.